$E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation

TL;DR

This paper extends previous work to calculate M1 and E1 radiative transitions involving heavy-light quarkonia using Bethe-Salpeter equations, providing more rigorous formulations and decay width evaluations with comparisons to existing data.

Contribution

It introduces a more rigorous Bethe-Salpeter framework for calculating radiative transitions in heavy-light quarkonia, including excited states, with analytic decay width formulas.

Findings

Decay widths calculated for M1 and E1 transitions.

Results compared with experimental data and other models.

Analytic solutions for wave functions used in decay calculations.

Abstract

This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} \gamma$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}\gamma$, and $0^{-+}\rightarrow 1^{+-} \gamma $ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work, we make use of leading Dirac structures in the hadronic Bethe-Salpeter wave functions of the involved hadrons, which makes the formulation more rigorous. We evaluate the decay widths for both the above mentioned $M1$ and $E1$ transitions. We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $1^{--}$,$0^{-+}$ and $1^{+-}$ heavy-light quarkonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. We have compared our results with experimental data, where ever available, and other models.